On a more serious note, I think there are a lot of ways to handle their differences, but one thing I think is clearly significant is that Clerics get the free ritual casting feat where Paladins start with training in the heaviest armor in the game and shields. The Paladin is clearly the combat specialist to the clerics combat trained medic and officer.

I think that depends on how you construct your World as a GM and how the players want the Class to act- if they play Pallies as Jocks and Clerics as Nerds, then the populous will have a pretty good distinction. If it is rare to even see a Classed character OR if the classes basically act close together (under some over-arching Theology and Dogma, likely), then it'd be more like how most people differentiate between SWAT and a detective: with their work-clothes on.

Well, if you look at the religions in dnd in a way that is vaguely resembling the real world catholic orders (and the cleric and paladin share an origin in those cultural whereabouts), it's relatively simple:

Cleric: he's a real priest. He takes all the vows, is fully ordained, is a part of the church's power chain/structure (i.e. could become bishop, or equivalent), and normally administers sacraments, sanctifies weddings, blesses the cattle, and so on. He's the guy that preaches in the temple.[*]

Paladin: he's a soldier. He's taken only some of the vows and cannot preach, or administer sacraments. He's a man of faith, but not a priest. Basically, it's modeled after the Teutonic Knight, or the Templar Knight. They took only some of the vows of the monastic orders, and were militant orders.
[*] and yeah, DnD's cleric is much more 'action oriented', what with all that mace swinging and kobold bashing, but let's say that in a world with so many deities and dangerous creatures you can expect a priest to take some interest in his personal safety while traveling through the heathens

I think their roles as defenders vs. leaders are part of the answer, even if it's a bit metagamey. To put it simply, cleric is to paladin what warlord is to fighter. I can easily see a cleric leading a company of paladins in holy battle.